First of all, any attempt at trying to deal with a black hole mixing concepts of special relativity and "mass based" gravity is doomed. Black holes cannot be described in the flat spacetime of SR, nor is mass the source of spacetime curvature in GR - the stress energy tensor is.

Second, as already mentioned, relativistic mass has been the cause of probably almost as many misunderstandings of SR as the relativity of simultaneity. It is also an archaic concept that is not really used by practicing physicists.